A comprehensive implementation of dynamic time warping (DTW) algorithms. DTW computes the optimal (least cumulative distance) alignment between points of two time series. Common DTW variants covered include local (slope) and global (window) constraints, subsequence matches, arbitrary distance definitions, normalizations, minimum variance matching, and so on. Provides cumulative distances, alignments, specialized plot styles, etc.

## Project description

Comprehensive implementation of Dynamic Time Warping algorithms.

DTW is a family of algorithms which compute the local stretch or compression to apply to the time axes of two timeseries in order to optimally map one (query) onto the other (reference). DTW outputs the remaining cumulative distance between the two and, if desired, the mapping itself (warping function). DTW is widely used e.g. for classification and clustering tasks in econometrics, chemometrics and general timeseries mining.

This package provides the most complete, freely-available (GPL) implementation of Dynamic Time Warping-type (DTW) algorithms up to date. It is a faithful Python equivalent of R’s DTW package on CRAN. Supports arbitrary local (e.g. symmetric, asymmetric, slope-limited) and global (windowing) constraints, fast native code, several plot styles, and more.

## Documentation

Please refer to the main DTW suite homepage for the full documentation and background.

The best place to learn how to use the package (and a hopefully a decent deal of background on DTW) is the companion paper Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package, which the Journal of Statistical Software makes available for free. It includes detailed instructions and extensive background on things like multivariate matching, open-end variants for real-time use, interplay between recursion types and length normalization, history, etc.

To have a look at how the dtw package is used in domains ranging from bioinformatics to chemistry to data mining, have a look at the list of citing papers.

Note: R is the prime environment for the DTW suite. Python’s docstrings and the API below are generated automatically for the sake of consistency and maintainability, and may not be as pretty.

## Features

The implementation provides:

• arbitrary windowing functions (global constraints), eg. the Sakoe-Chiba band and the Itakura parallelogram;
• arbitrary transition types (also known as step patterns, slope constraints, local constraints, or DP-recursion rules). This includes dozens of well-known types:
• partial matches: open-begin, open-end, substring matches
• proper, pattern-dependent, normalization (exact average distance per step)
• the Minimum Variance Matching (MVM) algorithm (Latecki et al.)

In addition to computing alignments, the package provides:

• methods for plotting alignments and warping functions in several classic styles (see plot gallery);
• graphical representation of step patterns;
• functions for applying a warping function, either direct or inverse;
• a fast native (C) core.

Multivariate timeseries can be aligned with arbitrary local distance definitions, leveraging the [proxy::dist](https://www.rdocumentation.org/packages/proxy/versions/0.4-23/topics/dist) (R) or [scipy.spatial.distance.cdist](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.cdist.html) (Python) functions.

## Citation

When using in academic works please cite:

1. Giorgino. Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package. J. Stat. Soft., 31 (2009) doi:10.18637/jss.v031.i07.

When using partial matching (unconstrained endpoints via the open.begin/open.end options) and/or normalization strategies, please also cite:

1. Tormene, T. Giorgino, S. Quaglini, M. Stefanelli (2008). Matching Incomplete Time Series with Dynamic Time Warping: An Algorithm and an Application to Post-Stroke Rehabilitation. Artificial Intelligence in Medicine, 45(1), 11-34. doi:10.1016/j.artmed.2008.11.007

## Source code

Releases (stable versions) are available in the dtw-python project on PyPi. Development occurs on GitHub at <https://github.com/DynamicTimeWarping/dtw-python>.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

### Credits

This package was created with Cookiecutter and the audreyr/cookiecutter-pypackage project template.

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